The Kumaraswamy Burr XII distribution: theory and practice

Abstract

For the first time, a five-parameter distribution, called the Kumaraswamy Burr XII (KwBXII) distribution, is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the logistic, Weibull and Burr XII distributions, among several others. We obtain the complete moments, incomplete moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and reliability of the KwBXII distribution. We provide two representations for the moments of the order statistics. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the KwBXII distribution. Three applications to real data sets demonstrate the usefulness of the proposed distribution and that it may attract wider applications in lifetime data analysis.

Keywords:

• Burr XII distribution
• Kumaraswamy distribution
• maximum likelihood
• observed information matrix
• order statistic
• Weibull distribution

Acknowledgements

The authors are grateful to two anonymous referees and the Editor for very useful comments and suggestions. This work was supported by CNPq and CAPES, Brazil.